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We obtain a recursive formulation for a general class of optimization problems with forward‐looking constraints which often arise in economic dynamic models, for example, in contracting problems with incentive constraints or in models of optimal policy. In this case, the solution does not satisfy the Bellman equation. Our approach consists of studying a recursive Lagrangian. Under standard general conditions, there is a recursive saddle‐point functional equation (analogous to a Bellman equation) that characterizes a recursive solution to the planner's problem. The recursive formulation is obtained after adding a co‐state variable μ t summarizing previous commitments reflected in past Lagrange multipliers. The continuation problem is obtained with μ t playing the role of weights in the objective function. Our approach is applicable to characterizing and computing solutions to a large class of dynamic contracting problems.

Dealing with out-of-equilibrium behaviors of economic agents is necessary to fill in the gaps in the controversy surrounding the admissibility of the fiscal theory of the price level (FTPL). Incorporating Nash equilibrium into the theory serves this purpose. It turns out that under certain conditions, strategic interaction between a non-Ricardian benevolent government and households with tit-for-tat moves leads to an equilibrium consistent with the FTPL, where the non-Ricardian optimal fiscal policy is not globally viable. Implementability of the non-Ricardian policy depends on the stochastic properties of government expenditure, especially its variance.

The Great Recession challenged the conventional way of conducting monetary policy and sparked debates on optimal monetary policy in the presence of the zero lower bound on nominal interest rates, and its interaction with asset prices in financial market. My dissertation shows how the zero lower bound changes the conduct of monetary policy, and how considering asset prices in monetary policy helps to improve the welfare of the economy. In Chapter 1, I first examine the role of money in precautionary saving and the behaviour of other asset prices, such as returns on bonds and stocks. Money is introduced via the form of transaction cost into a production economy with limited stock market participation, where agents with a lower inter-temporal elasticity of substitution, called "non-stockholders", have no access to the stock market. This model not only quantitatively resolves the risk premium puzzle and the risk-free return puzzle and matches volatilities of key macroeconomic variables, but also corresponds with empirically documented facts regarding money growth, inflation, and asset prices in the literature. I then examine whether money growth should respond to equity prices and equity premiums. I find that monetary policy improves welfare for both stockholders and non-stockholders if it reduces equity premiums in the economy. The model thus prescribes money growth rules that are pro-cyclical with respect to equity prices or equity premium changes. Chapter 2 studies how the conduct of monetary policy affects the frequency of the zero lower bound binding in a canonical New-Keynesian Dynamic Stochastic General Equilibrium (DSGE) model. The model generates a much deeper recession if the zero lower bound binds than when it does not. The model economy almost never hit the zero lower bound if monetary policy is described by a Taylor rule with interest rate smoothing. Increasing the central bank's reaction to deviations of inflation and output does not increase the probability of the economy hitting the zero lower bound. With interest rate smoothing, a lower inflation target significantly increases the likelihood of the economy hitting the zero lower bound. I also show that linear approximation solutions fail not only quantitatively but also qualitatively in analyzing the zero lower bound. The final chapter explores the role of credibility and what optimal policy the central bank can credibly make for forward guidance by solving for the whole set of sustainable sequential equilibria (SSE) in a standard New Keynesian model with an occasionally binding constraint on the nominal interest rate. Under full commitment, forward guidance is a longer duration of nominal rates at zero even when the contractionary shock disappears, followed by a quick revert-to-normal path. However, under the best SSE, there are many different policy paths that can be interpreted as forward guidance. One possible policy path features a smaller decrease of the nominal rate when the contractionary shock happens and an even longer duration at the zero lower bound than under full commitment. Another policy path keeps the nominal rate away from zero all the time and results in smaller inflation. The economy reverts more slowly to its normal state under the best SSE. The key insight is that central banks with same credibility may choose very different policies in their forward guidance and they do not have to lower nominal rate to zero. The full commitment equilibrium is not generally implementable.

2012～2016年度科学研究費補助金[基盤研究(S)]「長期デフレの解明」(研究代表者 東京大学経済学研究科・渡辺努, 課題番号：24223003)

We consider an economy where individuals face uninsurable risks to their human capital accumulation and analyze the optimal level of linear taxes on capital and labor income together with the optimal path of government debt. We show that in the presence of such risks, it is beneficial to tax both labor and capital and to issue public debt. We also assess the quantitative importance of these findings, and show that the benefits of government debt and capital taxes both increase with the magnitude of idiosyncratic risks and the degree of relative risk aversion. (JEL D52, H21, H24, H25, H63, J24) Human capital is an important component of wealth both at the individual and aggregate level, and its role has been investigated in various fields in economics. In public finance, Jones, Manuelli, and Rossi (1997) show that the zero-capital-tax result of Chamley (1986) and Judd (1985) 1 can be strengthened if human capital accumulation is explicitly taken into account. Specifically, they demonstrate that, in a deterministic economy with human capital accumulation, in the long run not only capital but also labor income taxes should be zero, hence the government must accumulate wealth—that is, public debt be negative—to finance its expenditure.

Most economic models do not suggest an optimal fiscal policy in which the government's budget is balanced each period. Conventional wisdom suggests that the government run surpluses and deficits to smooth taxes. In this paper, I use an approach which brings together real business cycle theory and the theory of public finance to evaluate the effects of a balanced-budget restriction. Four fiscal policies are investigated in a model with growth. All models are solved numerically using a multidimensional collocation parameterized expectations algorithm. The welfare consequences of each policy are measured, and the optimal Ramsey policies are characterized. Journal of Economic Literature Classification Number: E62.

Studying a one-sector economy populated by finitely many heterogeneous households that are subject to no-borrowing constraints, we confirm a conjecture by Frank P. Ramsey according to which, in the long run, society would be divided into the set of patient households who own the entire capital stock and impatient ones without any physical wealth. More specifically, we prove (i) that there exists a unique steady state equilibrium that is globally asymptotically stable and (ii) that along every equilibrium the most patient household owns the entire capital of the economy after some finite time. Furthermore, we prove that despite the presence of the no-borrowing constraints all equilibria are efficient. Our results are derived for the continuous-time formulation of the model that was originally used by Ramsey, and they stand in stark contrast to results that – over the last three decades – have been found in the discrete-time version of the model.

We obtain a recursive formulation for a general class of contracting problems involving incentive constraints. Under these constraints, the corresponding maximization (sup) problems fails to have a recursive solution. Our approach consists of studying the Lagrangian. We show that, under standard assumptions, the solution to the Lagrangian is characterized by a recursive saddle point (infsup) functional equation, analogous to Bellman's equation. Our approach applies to a large class of contractual problems. As examples, we study the optimal policy in a model with intertemporal participation constraints (which arise in models of default) and intertemporal competitive constraints (which arise in Ramsey equilibria).

We study the dynamic Ramsey problem of finding optimal public debt and linear taxes on capital and labor income within a tractable infinite horizon model with incomplete markets. With zero public expenditure and debt, it is optimal to tax the risky labor income and subsidize capital, while a positive amount of public debt is welfare improving. A steady state optimality condition is derived which implies that the tax on capital is positive, when savings are sufficiently inelastic to returns. A calibration of our model to the US economy indicates positive optimal taxes and a small but positive optimal debt level.

How should capital and labor be taxed when individuals' labor income is subject to unin- surable idiosyncratic risks? To address this question, we develop a tractable infinite horizon model with incomplete markets and consider a dynamic optimal taxation problem with linear taxes on the wage and interest income. We derive two general principles for public policy in such an environment: (i) providing an insurance for the idiosyncratic income risks; and (ii) allocating tax burdens efficiently over time. The first principle calls for taxing the labor income. The second principle clarifies when accumulating government debt is welfare improving, and also when the tax rate on physical capital needs to be strictly positive in the long run. We also calibrate our model to the U.S. economy and find that the presence of idiosyncratic income risks significantly affects the optimal tax rates and the optimal amount of the government debt.

This paper studies the optimal rate of seigniorage in an economy characterized by decentralized trade and a tax-evading underground sector. The economy has buyers, some of whom visit the formal market, while others visit the underground market. I find that the optimal rate of inflation depends on which of the two sectors, formal or underground, is more crowded/congested with buyers. If the underground sector is more crowded, the optimal inflation rate is as high as 42% per annum for Peru. That is, I offer a possible motivation for the high rates of inflation observed in that country from the mid 1970s up to the mid 1990s. If the formal sector is more crowded, optimal inflation falls to about 1.4%, which is close to the rate in 2005. Friedman rule is not optimal.

This paper investigates how the feasibility of migration affects governments' optimal fiscal policies. We assume that households migrate toward economies where their welfare is higher, governments choose taxes and public expenditures to maximize a weighted sum of the households' welfare, welfare is increasing in public expenditures, and only distortionary labor income taxes are available. In isolated economies, the optimal fiscal policy implies that some households are net fiscal contributors, while other households are net fiscal beneficiaries. When households can migrate, however, governments compete for the households which are net fiscal contributors, and modify the fiscal policy in their favor, lowering their taxes and net fiscal contribution, and increasing their welfare. The magnitude of the effect increases with the sensitivity of migration to welfare. In the limiting case of free mobility, all households are zero net fiscal contributors. As to the patterns of migration, the model predicts that, with high migration costs, all households migrate toward the same high-productivity countries, which benefits low-productivity households, whereas with low migration costs, households with different productivities migrate toward different countries, which benefits high-productivity households.

How should taxes, government expenditures, the primary and fiscal surpluses and government liabilities be set over the business cycle? We assume that the government chooses expenditures and taxes to maximize the utility of a representative household, utility is increasing in government expenditures, only distortionary labor income taxes are available, and the cycle is driven by exogenous technology shocks. We first consider the commitment case, and characterize the Ramsey equilibrium. In the case that the utility function is constant elasticity of substitution between private and public consumption and separable between the composite consumption good and leisure, taxes, government expenditures and the primary surplus should all be constant positive fractions of production, and both government liabilities and the fiscal surplus should be positively correlated with production. Then, we relax the commitment assumption, and we show how to determine numerically whether the Ramsey equilibrium can be sustained by the threat to revert to a Markov perfect equilibrium. We find that, for realistic values of the preferences discount factor, the Ramsey equilibrium is sustainable.

This paper investigates how the feasibility of migration affects governments' optimal fiscal policies. We assume that households migrate towards economies where their welfare is higher, governments choose taxes and public expenditures to maximize a weighted sum of the households' welfare, welfare is increasing in public expenditures, and only distortionary labor income taxes are available. In isolated economies, the optimal fiscal policy implies that some households are net fiscal contributors, while other households are net fiscal beneficiaries. When households can migrate, however, governments compete for the households which are net fiscal contributors, and modify the fiscal policy in their favor, lowering their taxes and net fiscal contribution, and increasing their welfare. The magnitude of the effect increases with the sensitivity of migration to welfare. In the limiting case of free mobility, all households are zero net fiscal contributors.

How should taxes, government expenditures, the primary and fiscal surpluses and government liabilities be set over the business cycle? We assume that the government chooses expenditures and taxes to maximize the utility of a representative household, utility is increasing in government expenditures, only distortionary labor income taxes are available, and the cycle is driven by exogenous technology shocks. We first consider the commitment case, and characterize the Ramsey equilibrium. In the case that the utility function is constant elasticity of substitution between private and public con- sumption and separable between the composite consumption good and leisure, taxes, government expenditures and the primary surplus should all be constant positive frac- tions of production, and both government liabilities and the fiscal surplus should be positively correlated with production. Then, we relax the commitment assumption, and we show how to determine numerically whether the Ramsey equilibrium can be sustained by the threat to revert to a Markov perfect equilibrium. We find that, for realistic values of the preferences discount factor, the Ramsey equilibrium is sustain- able. Keywords: Fiscal policy, Commitment, Time-consistency, Ramsey equilibrium, Markov perfect equilibria, Sustainable equilibria.

ÖZET EN İYİ SERMAYE KAZANÇLARI VERGİSİNİN UZUN OMURLU ÇAKIŞAN NESİLLER MODELİNDE BELİRLENMESİ Orkhan Hasanaliyev Ekonomi Bölümü Yüksek Lisans Danışman: Dr. Sabit Khakimzhanov Temmuz 2001 Bu araştırma uzun ömürlü çakışan nesiller ekonomilerinde hükümet farklı nesillerin sermaye ve emek kazaçlarını farklı vergilendirebilme mekanizmasına sahihken ve böyle bir mekanizmadan yoksunken, sermaye kazaçlannın optimal vergilendirmesini ele almaktadır. Böyle bir ekonomide, hükümet sözüne sadıkken, her iki durum için de optimal verginin sıfır olduğu bulunmuştur. Fayda fonksyonu toplamaya göre ayrılabilir olduğu durumu için, hükümet farklı nesilleri farklı vergilendirme olanağına sahihken geçiş döneminde dahi sermaya kazanç vergisi sıfır olarak bulunmuştur.' Anahtar kelimeler ve ifadeler. Optimal Vergilendirme, Çakışan Nesiller, Ramsey Dengesi, Taahhüt Teknolojileri. iv TOP WKSmOGRCTM KMMM* TOEtoAHTASYOI* Mmm ABSTRACT OPTIMAL CAPITAL INCOME TAXATION IN INFINITELY-LIVED OVERLAPPING GENERATIONS ECONOMIES Orkhan Hasanaliyev M. A. in Economics Advisor: Assist. Prof. Dr. Sabit Khakimzhanov July 2001 This paper analyzes optimal capital income taxation in infinitely-lived overlapping generations economy for both cases when government has the ability to tax capital and labor income of individuals of different vintages differently and when it has no such an ability. In such an economy with the commitment technology I find that optimal long-run capital income tax is zero fot both cases. For a special caso of additively seperable utility functions, I find that if the government has rich set of fiscal instruments, then capital income tax is zero even along the transition path. Keywords and phrases: Optimal Taxation, OLG, Ramsey Equilibrium, Commitment Technology. in 30